A056978 Number of blocks of {1, 0, 0} in binary expansion of n.

0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1

Offset

1,36

Comments

a(n) = A213629(n,4) for n > 3. - Reinhard Zumkeller, Jun 17 2012

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Digit Block

Formula

a(2n) = a(n) + [n congruent to 2 mod 4], a(2n+1) = a(n). - Ralf Stephan, Aug 22 2003

Mathematica

a[1] = a[2] = 0; a[n_] := a[n] = If[OddQ[n], a[(n-1)/2], a[n/2] + Boole[Mod[n/2, 4] == 2]]; Table[a[n], {n, 1, 102}] (* Jean-François Alcover, Oct 22 2012, after Ralf Stephan *)
Table[SequenceCount[IntegerDigits[n, 2], {1, 0, 0}], {n, 120}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 01 2016 *)

Prog

(Haskell)
import Data.List (tails, isPrefixOf)
a056978 = sum . map (fromEnum . ([0, 0, 1] `isPrefixOf`)) .
                    tails . a030308_row
-- Reinhard Zumkeller, Jun 17 2012
(PARI)
a(n) = hammingweight(bitnegimply(n>>2, bitor(n>>1, n)));  \\ Gheorghe Coserea, Sep 08 2015

Crossrefs

Cf. A014082, A056974, A056975, A056976, A056977, A056978, A056979, A056980.

Sequence in context: A086075 A316865 A325616 * A321761 A037819 A090405

Adjacent sequences: A056975 A056976 A056977 * A056979 A056980 A056981

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved